Research Interests:

My main research work is in the field of infectious disease modeling. The focus in my work is on the mitigation and control of diseases by vaccination and culling. I studied the dynamics of several diseases: COVID-19, MERS-CoV, pertussis, and measles in humans, as well as mad cow disease and chronic wasting disease in animals. I used various dynamical and mechanistic modeling approaches: deterministic (e.g., ordinary differential equations (ODE), fractional differential equations (FDE)) and/or stochastic (e.g., continuous-time Markov chains (CTMC), discrete-time stochastic simulation, fractional stochastic processes, multi-type branching processes (MBP)), as well as probabilistic modeling approach. I also model human behavior towards control measures using behavioral game theory. My choice of the modeling approach is based on the type of research question. In several papers, case data was used to either calibrate or validate the model, using a statistical measurement model. I use the maximum likelihood method or least squares to estimate the parameters. In others, a Bayesian approach is being used. 

Research questions in environmental science and ecological science as well as measurement error adjustment in risk of exposure are also of interest to me. In those studies, the research work involved statistical modeling (like zero-inflated Poisson modeling of counts, and Berkson error model in retrospective case-control studies) that were analyzed using maximum likelihood method and Bayesian methods. 

I have also miscellaneous research efforts that might be extended to study machine learning and deep learning; in particular, my work on exact and numerical solution of stochastic partial differential equations. We introduced a new term stochastic mesh, on which numerically solving specific types of deterministic PDEs gives a numerical approximation to the solution of their counter SPDEs. I have also interesting experience with random matrices and random walk on random trees.

Workshops and Conferences: TBU


Master Students: TBU

  • Currently advising four students for master thesis
  • Committee chair for one master thesis students in 2016 (defended successfully)

Undergraduate Students: TBU

  • Ruben Salinas – Modeling externality of disease and poverty (Fall 2016)
  • Christian Duarte Vela – Agent-based network models of paediatric disease spread and vaccination opinion diffusion under social influence (Summer 2016)
  • Oziel Pulido – Statistical analysis of human organ donation disparity (Fall 2015)
  • Margarita Garza – Trans-boundary meningococcal disease control (Fall 2014)
  • Antonio Vergara – Bayesian homicide mapping for California state (Fall 2014)

Honor Student Project:

  • Jose Nunez – Markov chain and random walk (Fall 2015)

High Scholar Summer Project:

  • Agent Based Modeling of Nosocomial MERS-CoV Epidemic (Summer 2016)